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Ranking patterns of unfolding models of codimension one

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Title: Ranking patterns of unfolding models of codimension one
Authors: Kamiya, Hidehiko Browse this author
Takemura, Akimichi Browse this author
Terao, Hiroaki Browse this author
Keywords: All-subset arrangement
Braid arrangement
Characteristic polynomial
Finite field method
Hyperplane arrangement
Ideal point
Mid-hyperplane arrangement
Ranking pattern
Unfolding model
Issue Date: Aug-2011
Publisher: Elsevier
Journal Title: Advances in Applied Mathematics
Volume: 47
Issue: 2
Start Page: 379
End Page: 400
Publisher DOI: 10.1016/j.aam.2010.11.002
Abstract: We consider the problem of counting the number of possible sets of rankings (called ranking patterns) generated by unfolding models of codimension one. We express the ranking patterns as slices of the braid arrangement and show that all braid slices, including those not associated with unfolding models, are in one-to-one correspondence with the chambers of an arrangement. By identifying those which are associated with unfolding models, we find the number of ranking patterns. We also give an upper bound for the number of ranking patterns when the difference by a permutation of objects is ignored.
Type: article (author version)
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 寺尾 宏明

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